Characterization of self-adjoint extensions for discrete symplectic systems

All self-adjoint extensions of minimal linear relation associated with the discrete symplectic system are characterized. Especially, for the scalar case on a finite discrete interval some equivalent forms and the uniqueness of the given expression are discussed and the Krein–von Neumann extension is described explicitly. In addition, a limit point criterion for symplectic systems is established. The result partially generalizes even the classical limit point criterion for the second order Sturm–Liouville difference equations.